There are many instances in which certain parameters, which may be dynamically changing with respect to each other, must be coordinated or synchronized at a particular point in time. Such situations may occur in both mechanical machines or electrical circuits. For example, two objects, such as airplanes, rockets or other moving objects may be desired to rendezvous at a certain point, where each object has a varying trajectory and/or velocity. In another example, electrical signals often require synchronization of one signal with another having a varying frequency.
In the mechanical example, the point and time of rendezvous can be calculated utilizing numerous algorithms and differential equations to define the end objectives. In the electrical example, fewer techniques are available for accomplishing the synchronization of the signals. Conventional phase-locked loops (PLL) are well adapted for creating an output frequency as a function of an input frequency. Such phase locked loops employ a phase detector, a low pass filter and a voltage controlled oscillator and a feedback loop. .In this type of phase-locked loop, any difference between the input and output signals generates an error signal which is self correcting by the loop to maintain correspondence between the input and output. However, conventional phase-locked loops operate optimally when the input frequency does not vary substantially, thereby maintaining control over the error signal. If the input signal varies significantly in frequency or phase, the accumulation of errors become too great, whereupon the circuit is not able to maintain an established phase relationship.
The problems noted above are particularly pronounced in particle accelerators when transferring a particle bunch from one accelerator to the other. It is well known that particle bunches can be accelerated by utilizing magnetic fields and an RF signal which increases in frequency to achieve particle bunch acceleration. The problem exists in synchronizing the frequency of one accelerator to the other when transferring a particle bunch therebetween. In other words, a particle bunch circulating with others in a particular location in one accelerator is required to be transferred at a particular location in the next accelerator. Preferably, it is desired to operate the receiving accelerator at a steady state RF frequency during transfer, and sweep or modulate the frequency of the first accelerator from f.sub.1 to f.sub.2 to accomplish acceleration, and also to synchronize the frequencies of both accelerators together during particle bunch transfer. The synchronization problem is also exacerbated in that synchronization of the frequencies must occur during the maximum magnetic field within the first accelerator.
It is well known that two schemes are generally available for achieving synchronous transfer of bunched particle beams from one accelerator to the other namely, phase-locking and phase-slippage schemes. In the phase-locking scheme, at a known time before injection to the next accelerator, the phase and frequencies of the accelerating machine are locked to the extraction frequency. The time required to phase-lock the two frequencies depends on the lattice parameters of the accelerating machine. In the phase-slippage scheme, at a predetermined time before transfer, the frequency of the accelerating machine is offset a few cycles relative to the extraction frequency. The phase of the accelerating frequency slips relative to the fixed frequency, resulting in several phase coincidence points of the reference wave which occur at a beat frequency equal to the offset frequency. One of the coincident points is used to trigger the synchronous transfer of the beam.
From the foregoing, it can be seen that a need exists for a method and apparatus for obtaining and maintaining synchronization of parameters that vary with respect to each other. Another need exists for obtaining synchronization of a first frequency modulated signal with a second steady-state frequency signal, wherein the FM signal terminates with a frequency and phase equal to that of the steady-state frequency and phase.